{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basic (binary) GP Classification model\n",
    "\n",
    "\n",
    "This notebook shows how to build a GP classification model using variational inference. Here we consider binary (two-class, 0 vs 1) classification only (there is a separate notebook on [multi-class classification](../advanced/multiclass_classification.ipynb)). We first look at a one-dimensional example, and then show how this can be adapted when the input space is 2D."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gpflow\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "%matplotlib inline\n",
    "\n",
    "matplotlib.rcParams['figure.figsize'] = (8, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1D example\n",
    "\n",
    "First of all, let's have a look at the data. We denote by X and Y the input and output values. Note that `X` and `Y` must be two-dimensional numpy arrays, $N \\times 1$ or $N \\times D$, where $D$ is the number of input dimensions/features, with the same number of rows $N$ (one per data-point):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.genfromtxt('data/classif_1D_X.csv').reshape(-1, 1)\n",
    "Y = np.genfromtxt('data/classif_1D_Y.csv').reshape(-1, 1)\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(X, Y, 'C3x', ms=8, mew=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reminders on the GP classification\n",
    "\n",
    "For a binary classification model using GPs, we can simply use a `Bernoulli` likelihood. The details of the generative model are as follows:\n",
    "\n",
    "__1. Define the latent GP:__ we start from a Gaussian process $f \\sim \\mathcal{GP}(0, k(., .))$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# build the kernel and covariance matrix\n",
    "k = gpflow.kernels.Matern52(input_dim=1, variance=20.)\n",
    "x_grid = np.linspace(0, 6, 200).reshape(-1, 1)\n",
    "K = k.compute_K_symm(x_grid)\n",
    "\n",
    "# sample from a multivariate normal\n",
    "L = np.linalg.cholesky(K)\n",
    "f_grid = np.dot(L, np.random.RandomState(6).randn(200, 5))\n",
    "plt.plot(x_grid, f_grid, 'C0', linewidth=1)\n",
    "plt.plot(x_grid, f_grid[:, 1], 'C0', linewidth=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2. Squash them to $[0, 1]$:__ the samples of the GP are mapped to $[0, 1]$ using the logistic inverse link function: $g(x) = \\frac{\\exp(f(x))}{1 + \\exp(f(x))}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VhAuDr6sukUJHI05N5ojcz6m+zNVP/yiT1R1FawlNDBbjPO2bcou+5f2O7z8YPYZIqd1YG1401cN/vgP/vkmK2Y0+G763UKJiDPFRMETOqdfvgONvl6J8pZta1403tMKIe+0haXwwKkSCxMb5Pqs+TTIGk8W42TJBXVPsT9TpCGVbJISwT5BKnxlZUtfmw1/Za717PNK1qWRTdNtrLReYv0yDlc+L22DW/VK+wrhh7OOYm6WnwPrXpIIkwPv32n/nliYYcd/yPgw7SepeBGPT21Jm1RAbngx/WOnCv3d8Pzs+kwnOUFFK42ZLiNzG+R0/RjB6j5PuTeGoPwwLH4WHJkuI3uHdUob5lgUmsioReDLkovnhr6TccE6+1Jna8VmqR+ZIjLhv/1hSnYPh9cLOL2D4yckdU7oweQ6gZEK0urhj+9i/UrpohcLjgVP/Bxb81l7/a59xweOptZbIqRdvgPtHSMhn+Q7p1XrGvXDHSmmgYUgMg6bKhPeXfxFLHqSRiaEdRty3fyKWezCK10k7PlOVrmN06yM1U/AVyOoI+1dKpEw4xs4Sq27D6x07RjB6j5MOXBaNNWKlP3ik1LhZ96qENw44Gi59Au7enl4Fv5zMGfdK8cCxMwEl9Wgq96V6VI6jc4t7+U6ZBOs9Nvj6nV9IOQJDx7FyBxY/Fvt7W5qkC1HfCE1YlILTfmKv9d7bZ7nXlMK7/wsPjBIrvXKPrznLbRKzfusCmHhZcnuwdnZ6DJQyFF/+zRfooGHtqykelPPo3OK+41OxLEP5Rnd+Lo0HDB1n9DnSu7NiV/QTlBYlG6TZQ6j5kFbHOUu2W2dT9ETBUGlY/aeJ8MVDUmu89zi47Cm4azuc82tTOiCVnHC71IsfdIw8X/ViasfjQDq3uG//NLQ/XWtjudtBZra/PO+af8f23mhcMhZKSfzzZw/GHz2htTRd9zaJqA+cCt98V8Iaj7zElA1wAtl5Ehq5zVfzaf8KCV81fE3nFvedX/h8wkEo2woZ2RJfa4iPyVfLcuULsb0vFnEHiSv3tsDWD2I7Tlve/Ql85muWfdTVcPMHpmSAE5l0lbTbLBwBaEl2M3xN5xX36hJoOAy9RgVfv2+56bRkFyNOg8wu0hu0dEv079u3IjZxVwpm/AA+iyN6YslTUk8cJReLvhNMSKNTyciE0/5HYt/BuGba0HnFff8K6D859A/3wEroNym5Y0pXMrPF9w4SZRItpZtiz+488hKZKN+9OLb3gZQqfvO/5PHsB8VlZ6IwnM0RFwO+3/DOz01CUwCdV9z3LgsfP71/VWxWoyE8Ey+T5ZqXo9u+rlxcLHm9YjtORpZMtsUa+7x/FTx/pYjD9Fth2jek/G/l3tj2Y0gungw46YeybKoVd6oB6Mzivm95aHHXWup595uY3DGlMyNPA5UhsePR1GEv3yGlgzviEplyrTRZjrapQ8Vu6Y7U0gBjZkmbRZB2fsZydz6Tr5ZzC+R7NwBG3IOvq9wrZVq790vumNKZnO7+Dvabo+iFWb4DCod17FjZeTD9W9HVk6+rgKdmSSmBAVOk+qDH97PIH2DE3Q1k5vij3uyow58mdE5xr9wvYW6hImH2r5KyrwZ7mXi5LFdH4Zo5tD2+htHTb4YNb0rtkVB4vfDi9VITpmAIXPef1slI3fpJ2YSW5o6Pw5AcpvuS5eKtw59GdE5xt6z2kJOpq8xkaiIYO0uWOz6F5obw25bvgJ7DO36s3J7invnyr6G3+eQBsfQyc+GG1+U9gWRmS934mg7WxTEkj+EnAwqq9sVeqjlN6ZzifmB1+JT2A6uNvz0RFAyRWuktjZEr+ZXHabkDHP89WPG8lHVuy7aP4CNfv9fLnw59LOOacQdZXaDnUHm8a1Fqx+IQOqe4F6+DvkeEXl+yIXj9cEP8HHGxLNe9Fn47a0I1HvIHwPjZsOjR1q8f3gtzrwE0nHCHrwBVqH0MNBEzbmGEr7rr2hgzodOUTiru60OLd3OjRE8UxuESMITG6lO74Y3QMcktTVB1wJ7s4BPukObnjTXyvLkRnr8cGqth0HQ482fh328sd/dgBUjEm6GcJkQl7kqpmUqpjUqpLUqpe4KsH6KUWqCUWq6UWqWUOtf+odpEc4NkShaNDr6+fLtUnTNV/hLDwKmQ3Q1qy0L3Ka3YJZFKdtRw6T0Ghh4Py56R52/dJW0Tc3vCnBckPjocJtbdPViu1poSMQ46ORHFXSmVAfwVmAVMAOYopdqavT8FXtRaTwGuAv5m90Bto3ST3O6HEu/SzdJizZAYPB5J6wdYNy/4NvFOprbl+Nth4SOw6V1Y+pS0wbv6JanVHwkT6+4e+oyTpdaw4rnUjsUBRGO5Twe2aK23aa0bgblA227SGrCaRfYAnPtrOLgufEp76abQ9WYM9jDpSlmuCtHAo2KXvQXbBk+XOPuXbpTnp/4YBh8T3XvzB4iP3uB8srtK316Alf9K7VgcQGYU2wwEdgc83wO0LZH3c+BdpdTtQFfgTFtGlwiK14WfLC3bAoNNBcCEMvI0uXMq3yHp4m3rolcfhO797TueUpCVB001cut+0p3Rv7dbX7nNN7iDPuNhezFU7YdD23wVIxNIc6P0Yd6/Unr59hoN486LrgdBgrFrQnUO8LTWehBwLvBPpVS7fSulblVKLVFKLSkpSdEPJtxkKojlHsofb7CHzBx/IbFgCU1VB6RFn13sWepPSz/tfyL72QPJ6yXzAwZ3MHi6LAuGwFqbGrcEo6UZFj8uzdG//IskRaoMOeafJsLH90uXtxQSjbjvBQYHPB/key2Qm4AXAbTWXwJdgHYOTa31o1rraVrrab179+7YiOOleH1ot4zWPnE3PveE83WN9+fbr6sutq/0g9cLr35HHg86Bja9Hdv7u/SAhiqTpeoWrPwUbwusSZC47/wCHj1FWvtd+Sx8Y770dT3tx3D1XLjlA0mE/NuxsPw5if5KAdGI+2JgtFJquFIqG5kwbTsTtgs4A0ApNR4Rd+fdyzbWSrZhqPjpmlJAxV6J0BA7I0+XzNDyHXBgTet11QfEHWIH616F0o0i0pc8LvH1NTFY4p4MyC0wXX7cQh9f/krVfvmr2GXPfrWGXV/Bv66Df98srr0bXvfXSwqkcISI/gV/kQY1/+9oWPyE1DFKIhHFXWvdDNwGvAOsR6Ji1iql7lNKXeDb7E7gFqXUSuAF4EatHVhY+dA2EfZQt+WWS8Y0Z0g8mTn+MsCL/t56XXWxPeLe0gTv/Fgen/EzKUQ2bjYsezq2/RjXjHvoOUyioeorpHn2pnc6th+tJVP90z/Ac1fA/cPhtduk7eb3FknfgEg6MfwkuPENuOQx2PohPHgkPDkT3vmJnOMJJpoJVbTW84H5bV67N+DxOsD5naTLtoSPhKnYaW8IniE8x34Llv9TOujMuh+ycuVHVX3QHnFf/pz477v3g6Ov9x3z21K3/YTvRx9Hb8TdPWRkQtfecg71nywVSKffEts+9i6DebdDQyWMPVdciOf/GfI7OMk/5Dj5a6yRuZ99y6WFZ4KJStzThrLN4TvWV+zy16cwJJ5+EyW6oGwzrHkFplwj7o+sXKkVEg9eL3z8O3l81i/9Qt5/kmQfr3vNf+cQCSPu7qLnMF/EVV/Y+aW4Y7PzonvviufhvXvhnN/K+WHnXXx2V3FHjjzdvn2GoXOVHyjbGt5yL99pGmInmxl3yPLD+8SNYpfVvult8bnmFcIRl7Red9x3JKkpWvIKjbi7CStgouoADJgM2z+J7n2b3oX3fgY3zodJl7vePdvJxH2LWIqhsDt5xhCZo66SuulVB8RFY5e4f/QbWc74odyqBzL2XDlOtH1WjeXuLnr7xL14HYw6M7paM6Wb4dVvw1XPS8mKNKATins4n/suKDBumaSSkQXn/Foev/8LuXuKV9z3LpXJsMwcmHpD+/WeDDjue/Dl/4tuf3m9gpcNNjgTy/VavEES5rZ9FH77pjrJXj7tJ9FnLruAziPutYfEDxuqnkhLk9zG5w9M7rgM4jbpNVoiHJY/G3+M+8f3y/LoG6FLfvBtplwrXXsObYu8P2O5uwsrK7ViJ/SdKN9duBISH/5KjL5p30zO+JJE5xH3Ut9kaig/WuVesRgzEz+LbWiDxwOXPgYo2LMIvHEkDJXvlPA35YEZ3w+9XU43mHojfBlFjTsj7u6ix2BAQd0hyRwdfnJo633fClj1LzjvD673sbel84h7NC4ZEymTOgZM8VtOa1/peEbo538GtPjVewwKv+2x34LVL0Z2uRhxdxeZ2f479PKd0sQjmLi3NMPr34ez7ouuQqjL6DziXr4jfAMOM5maes66DzyZkuDx5V9if39dhUzKApxyV+Ttu/eDcedL9mA4TLSM+7Dmzg5tk2SmbR+1bw6z8BHoUgBHzUny4JKD+8Td6tITK5EmS00YZOrJ6eYvGPbhr6QjViwseVL6sw44GvofFd17TrhN2vCFK/JkJlTdR29fbfdD2+SOPLtr6+Yw5Tsl+3T2g2nnjrFwn7gfXAvPRpl8Ekgky9xEyjiDpjqxtLxNMP+/o39fc6PPJYNUfoyWPuPFJWRZ/MHIyYfmeuniZXAHVvG/si2ybBs188EvJN8hXFKjy3GfuBcOl6txrKVrohJ3Y7mnFG8L1FfC7D+Le2bT27Djs+jeu/YVibbpMUhim2PhlLvgsz+FFm+lfK4ZY727hp6+37Il7iNOha0L5PGBNRIpddx3UzGypOE+ce/SQ1LTY2mg0Nwo1SDDhTlW7pHeqYbUUX9YXDOFw2DGD+S1126LPLmqNXzkKzVw8l2x32YPmga9x0rqeSg686Tq4T1y4XUTPXziXrFTlsNOkqqOzY2w4Ndw4n85oqFGInGfuIPEsUYTn2xRuVeyINtmKlpoDVU2d/8xxE5duTSuBjj5v0VQy7eLLz0c2z+W7XK6+1v4xcopd8Fnfwxde7szivuur+CxM+BvJ8D9IyQ13y0iX+BrQWFVX8wrhKJRsHKuFO5Ks5j2YLhT3HsOj03cI7lcasuksFBWbvxjM3Scugq/uGflwnl/lMfv/yy0S0RreP/n8vi473a84NiQ46Tg1KoQvTdze3YucS/ZBHOvEb/03dvhu19K5u+L14v163S69hbXXlOtNFsBCYn86i9w/G3xF6ZzAe4U98IRcGh79NtHEvfKvSYz1QkEWu4AEy6EgVPlB/rW3cHfs+UDscSyckWI4uGUu+GT3wd3A+UWiNuoM9BUBy9cKaGpEy+Tcg35A+Daf0s00nv3Rt5HqlHKH7tuRV0VjZbigVNvTNmwkomLxd1Gy71yv3HJOIG6csgt9D9XCi56RLJNV78Iuxa23t7rhbd+JI9Pvrv1haEjDDtRQjE3vdV+XZcenUfclzwlfYanXNP69cwcuPjvsPFNKZnsdHr4XDNWN6Y9iwEVXwa0i3CpuNvslqna1/FC/Ab7qDvUXqB7j4HjvyePX7yutXvm4/+T8yC3Jxz3bXvGcPT1wSdWO4u4N9VJSOkpIe6U8grhsqdg/o+S3jYuZqwaM4d3y93Y+tdh0NToI7BcjkvFPRGW+4D4x2WIj7ZuGYvTfiKFxaoPwnOXi8BvfFvEHaSNmV3zJRMuhB2ft2+D1qWTuGWW/kOih/pPCr3NoGlS3uHDXyVvXB2haKwsy7bA9o9EA8aeC9sWpHRYycKd4p7XC7Q3+rjjiOJuLHdHEErcs3Lh+lclGmbvEvj9aPEJo6V07+iz7BtDTncYdx6sfqn1653Bctcalv0juvjvM+6V5uPF6xM/ro5i/eZLN8Pql2HiFaHrzKQh7hR3pSSyoTyKSdWWZqg+IBNCoajaZyZUnUAocQdJTrrpfRh0jPhMM3PgpB/JpJ/dHHUlrPl369c6g7gfXAMN1TDk+Mjb5hVK4bUvoqyJnwoscS/fARvnwxEXQ98jxZ0Ua2kLF+LeHqqFwyViZuDU8NtVHxRLP1wzZDOh6gzCiTtAn3Fw8/tSgiJ/QPwTqKEYcjyUbBQx79JDXuvSQzJg05mVc6W9nCdKm2/aTfDQFN+drwPdmlase9U+cdF09zWBGXGKWO9HX5eyoSUDd1ruIDPhh6O4+lZFIdxVDj05OxuRxN2i7xGJE3aQu4KBU6W5skW6+9y9LeIZIR3eAAAgAElEQVS6iCUJLK9QKip+9XDixhUP3fpKpFVTneQxWIw4tVP43d0r7gVDJC06EpGsisYaqSmSSLEwREe04p4Mhp/curFyurtl9i6VO9zeY2N733Hflu5ZjbWJGVc8eDLkogz+yVXwifvHEkqbxrhX3HsMjs5vVnUgvOVeuV/qeqdp2U9XUXtIrEEn0NnEfcv7MDrGgmsgc1+Djmk/R+EUrJaN3QP68hYMke+zeG1qxpQkXCzug6J0y+wLL+5mMtUZeL0+H3dBqkciDJgiRaesiKysXHFdhKv77ma2vB97NU2L6bfA4sdir9SaDHJ8PXTrK1u/PuJUf5XINMW94l7gs9wjnVCV+8OHOVYdEN+cIbU0VEpDhVDF3ZJNRpZYpLu+kudKibXXUBn+fW6kplTCBQcfF3nbYIw8Q8RzzxJ7x2UHyidxbe/yR58lJaXTGPeKu2XhRbpVjmS515T4u/8YUkddudRvcRL9J8GB1f7n6eqa2bpASuJ2tDm8xwPH3CTWu9OwioYd2tL69RGnyXdbU5r8MSUJ94q7UmK9R3LNVO4PP6FaUyIV5AypxUmTqRb9JsKBVf7nXXo4P+W+I2z9EEadHt8+Jl8jlnB1DH0WkoGVadw2JyarC4w8XeLf0xT3ijuI3z3SpGqkCdVqI+6OwJHi3sZyT9fKkDs/F8s9HvIKYfz5sPwZe8ZkB/WV0OD7vir3tV8//nypN5OmuFzcI1juDVWSzWglogTDuGWcgRPFvXCE3LZbgp6OiUyH90Jjtb/naDxMuwmWPu2cEMODa/0hkME6t40+S3IZ0vGCjdvFPZJbxppMDRfmWFNsLHcn4ERx92RIA+2DvpC5dPS57/pSMnLtCAUeMAWyu8NOh1RdPLgGBkwGT5bksrSNmOnSA0aeCmteScnwEk1U4q6UmqmU2qiU2qKUuifENlcopdYppdYqpcI0o7SRSLHuVfsiV3usKTXi7gTqK8LfYaWKfhP9rpl0FPedX0RXSyYalIIp18Ly5+zZX7wcWCWT4lbuROXe9ttMuR6W/zO540oSEcVdKZUB/BWYBUwA5iilJrTZZjTwY2CG1voI4AcJGGt7IrllIoVBai0TLkbcU099pT8m2UkETqqmo7jv+hKGnmDf/iZdARvfcsb/6cBq6DvRH1BxOIi4jzpDdOLguuSOLQlEY7lPB7ZorbdprRuBucCFbba5Bfir1rocQGvdphh2giiIZLlHqCvTUCXxzNl59o/NEBsNldDFqeK+Rh6nm7jXHpLfT78wtdtjpWsRDD8p9ROVLc1QvAH6TpAsWghuCHoyYPLVaWm9RyPuA4HA/8oe32uBjAHGKKU+V0p9pZSaGWxHSqlblVJLlFJLSkpsCJnq1k9u50NlDVZFEwZZFP84DPFTXwk5DnTL9BolfTe1Tr/iYXuXwsAp9ieOHXFx6v3Y5dslUCKnOxSOktdCGYJTrpXG6M0NyRtfErBrQjUTGA2cCswBHlNKtctI0Vo/qrWeprWe1ru3Da4Qj0fEO5gvDST8yaotEQwT4+4cnGq55xVKck/1QZ+4p1G0zJ4lkUtmd4QxM6VfabTNdBJB6SZ/ETSr9G/Z5uDbFg6XnrEb3kzO2JJENOK+Fxgc8HyQ77VA9gDztNZNWuvtwCZE7BNPj8H+BrhtqYrQPq+6GLqaMEhH4FSfO/is9y3p55bZuwQGTrN/vzndJEFo/Tz79x0tpZulNSNIPgxIraBQHJ1+E6vRiPtiYLRSarhSKhu4Cmj7rb2KWO0opYoQN00MTU7jINykaqQJVeOWcQ4NVc603EFEIt3EXWtxywxKgLgDHHlJal0zpZuhqI24Vx0Ivf3482Hf8tCGoguJKO5a62bgNuAdYD3wotZ6rVLqPqXUBb7N3gHKlFLrgAXAj7TWZYkadCsKBgev6+5t8SUohXPLlJoEJqfQUCn+USfSa2T6ifuhbZDVNbzbMh5Gnw37VrRvNJ4sygLE3ar6WlsWutBgVi4ceRmsSE4UdzKIyueutZ6vtR6jtR6ptf6177V7tdbzfI+11vqHWusJWuuJWuu5iRx0K0LFuteUSLp4uGJIJoHJOTjeLbPVL+5OLG0bK3uXwsCjE7f/rFzJAF33WuKOEQqtpU2ilXWb0w0ycyVbvTaMzXn0dRKj75QM2zhxd4YqhM5SrYxQDRLMhKpT8LZAU42DLfdRcpuf1QVQ0JwGNd33LEmcS8biyEtg7X8Se4xgWBZ64G/behyue1v/o8Qg3P5RQoeXLNwv7qEmVKPpnWqKhjmDhipxEXgyUj2S4BQOl3OspTl9XDP7V0q5gEQy6kwpAVC5P7HHaYvlbw8sqWCFRIeKrLM4+nppG5gGuF/c8weKkHtbWr9euS/8ZCqYomFOwalhkBZZudLQpWKnWHZuL/vr9Uq9nH4TE3uczBwYe27yXTOlm/z+dovCEbKM1Hf5yEth8/tpcQF3v7hndZGCU9UHW78eKQwSjM/dKTjZ325R1Mbv7mbKt8tvJhmF2o64BNYmOWomcDLVotdIWZbvCP/evEJnZNjagPvFHYJPqlYdCG+5NzdCY41zenZ2ZpxuuYOksJfvSA9xP7A68Va7xYhTxZKOZDHbSdk2KBzZ+jUrHLJsa+T3T7oSViYvJiRRpIm4B2mWXRmhImRNCeQVSZarIbW4wXIvGCJuGSPusZGZDePOS+7E6qFtfkvd4utEpiji2MecI26rSI2A2lJ1AJY85W/tl2LSQ9l6DGo/UVIVRQJTN+OScQRusNwLhgaIu8t97skUd/C5ZpIk7l6v3GH1HN76dSvWvTpMIpNFZg5MvByWxdBVatFj8Lfj5HM+fIIkRKWY9BD3/IHt22hVRoiWMWGQzqHBDZb7ULH6jOUeO8NPgfKdkf3ddlC1XwyFnG6tX7eiZeoqJOopEsfcBMv+Ie7bSCx/Dj5/CG79CG6YByf/CN68M+X5EGki7m2KhzXWQEtD+AkjI+7Ood7B2akWPYeKQLld3GtK5fdRMCR5x8zIlPT+ZFjv5dvbW+0g1nhOPqDlAhCJ3mMlCWpDhInV/Svh/Z/Bda/4SwtPvlbO6R2p7UiVJuLexnKvOiBp1eFah5kmHc7BDW6ZvF7Q0ggZOe4W94Nroe8R9rTVi4Vk1Zo5tM0f9tgWy00bbf2YY26GhX8PvV5rmH8XnP7T1tE5Hg/MuAM++2N0x0kQaSLuA1qLe6TJVDCWu5Nwai33QJQSa7elyd0+95IN0Gdc8o87dIYYXdFEq8RDOHG3LPpoxX3cbDECd34RfP3ql6G5DqZc137dpCth/6rkuKJCkB7i3q2v3G62NMnzSJOpYIqGOQk3WO4gfvemWndb7sXroff45B/XkwETLoR1ryb2OIe2S0ZxMIp89d2jFdyMTDjxB/DpH9qva6iG9+6FWQ8Ez6zOzJbiaZveie5YCSA9xD0jU6xwK5Epqroyxi3jGNwQCgliuTdUuVvcU2W5A4yfDevfSOwxwlnuhcNkWbop+v0dNUcuiLsWtn790z/A8JNhyLGh3zt2Jmx6O/pj2Ux6iDu0ds1EU1fGuGWcg1ss955Doe6Qe8Vda5/lniJxHzpDJjyDNaq2A63DW+7WJPKhGFpNZObAzN/BK7f4y07s/AKWPg1n/jz8e0eeDrsXpSzuPc3E3XfSROOWMUXDnIObLPeaEveKe3UxKE/qzvuMLBh9Dmycn5j915TKXXyoKLmCobKsjDFbdsIFktj03OXwwS/hX9fCZU9E1pic7jDoGNj6YWzHs4k0EveBfougMkJdGa8XakuNuDsFt1juBUPk3HJrTfeS9dBnfPIjZQIZPztxdVuCJS8FYmWp1h5qX2gwEmf/GqZ9Q8o9X/2iWOXRMPps2PJBbMeyCZvbnqeQtm6ZcFfV+grI7hq+kYchebghiQkgfxBU7YOMbJlYze6a6hHFRvEGf9PoVDHyDPjPt8VVYXduQ8VOcZ2FIitXjtlQJRphiX00ZGbD5KtjH9OQY1NWQjiNLHefW8br9cW5R8pONZEyjkBr3w/dBeKe10sSgHLy3emaKUlRpEwg2XkwcCps/9T+fZfv8LteQmG1FUxWr9S+E2WeIQV+9zQSd18iU22pXJ0zc0JvaxKYnENjNWR2EV+p0/F4RByy89xZ071kY+otd4BRZyTGDx3Jcgd/FmmsRcE6Sma2JI2loNZMGom7zy1Ttd9fRyIUpmiYc3DLZKpF9wHuzVIt29K+znkqGHl6YsS9fGdky/3rWPft9h8/FIOOkbaGSSZ9xL17f4lzr9hrwiDdhFsmUy3y+4Mn033iXlcBTXWRfxvJoO+R4qawO3uzYqffMg+FVQq4eL29xw7HwKlG3OMiM1u6qJRtjK69nhF3Z+BGy10p94l72RYRtlRGylgoZb/13tIsd+6RJkmtBKfSzfYdOxKDjoG9S5IeYZU+4g7ijindaurKuAk3Wu7a61JxH5XqUfixW9wr98pvOtxcG/hDJds290kkBUPknInUnNtm0kzcB8LhnSaByU3UH3aZ5d5fqkO6TdxLN0MvB/jbLUaeBts/ia62ejRUROFvB7HslUeMisYae44dCaVkUvXguuQcz0eaifsAqIwQBgm+CVUTCukIXGe5DxDftdsqQzplMtWiWx+xaPcutWd/5VFEyoAU+bJ++8ms2NhnAhSvTd7xSEdxryszRcPchOt87v0lfNON4t62r2iqGXk6bLUpezNayx2gYJgsY6kxEy99JhjLPS7yB4olGDEU0pQecAwNVdLdyC107y8XJDfFuXu9UkfdST53kGxVu/zu0VruICUYAMqSKO59J0CxEfeOk9dLfHh5vUJv01grdd+d3tats+CW0gMWWV0kiam2NNUjiZ7KvZBb4LxzfshxEpJox/xFLJa7Je4lSRTb3uPl7snqOZEE0kvcPZmSRRgu3MvytzshJMzgjv6pbenaG2rLUj2K6Cnb7DyrHSSyZcCU9rXSO0J5FDHuFlY4ZPHG+I8bLdl54lFIdCeqANJL3L1e/18oakqga1HyxmQIj9smVEFcM3UuipYpdVgYZCDDToSdcTaSbqqDuvLoE7S+bre3M77jxkqSJ1WjEnel1Eyl1Eal1Bal1D1htrtUKaWVUtPsG2IM1JVJzehwVpUpGuYs3DahCtBjsEyqugWnRcoEMnQG7Pg8vn1U7JIQR0+UtmrBEEDJBaG5Ib5jx0KSwyEj/jeUUhnAX4FZwARgjlJqQpDtugN3ADbcY3WQqv0iFOGSBUzRMGfRcNh9lnvBULEW3VLT3aluGYBB08Tv3hDHxTKWyVTwZbP3AnTyqkOCdMAq2ZC0w0VzqZsObNFab9NaNwJzgQuDbPdL4P+AehvHFxuV++VLs+q6B8MUDXMWrrTcB0q8tFusdye7ZbJyof9RsDsOmzCWyVSLgsGyTGY4ZNFouYtKEtGI+0AgMFd3j++1r1FKHQ0M1lq/aePYYqfK1xg7nOVuSg84i4ZKd4VCgkyMqQx3hEM21UlBvVjFL5kMmwE743DNlO+IzXIHf137Q0msDlk4UsYaaxeoDhL3hKpSygP8Ebgzim1vVUotUUotKSkpiffQ7ancL19yuLoRRtydg9butNytiTs3lCA4tE1+E06ulx+v370jlvvX4ZBJrA6ZnSfakyRXUDTivhcYHPB8kO81i+7AkcBHSqkdwHHAvGCTqlrrR7XW07TW03r3ToDAVu2HojFwOEwDXCPuzqGpVibA3dbuMH8AeJvdIe5OqykTjMHT4cAqyUHpCLH63CE1pX+t4ybJNRONuC8GRiulhiulsoGrgHnWSq31Ya11kdZ6mNZ6GPAVcIHWOrkFjLWW9nr9jgzfZcUUDXMObmmv15bcnoAWd4fTKdsCRQ71t1tkd5Ua73sWdez9FTv9JQWixQqHTGZ9GZBxrpuXlCidiOKutW4GbgPeAdYDL2qt1yql7lNKXZDoAUZN7SGZnCkcGcEtU2yKhjkFNyYwgSTAZeUmN9Kiozit1G8ohnXQNVNXIT7svMLY3mclPNWU2FeZMhxlW6Ux+MrnYct7ErWXYKLyuWut52utx2itR2qtf+177V6t9bwg256adKsdRNB7DBZ/aE0pNDe236alSW6lw5UnMCQPNyYwWeR0h8PJrc/dIdzglgEYemLHJlUtf3usGefZeTKRr71QGcaNGy+V++G12+DxM+Vu4dLHJWqmYHDk98ZJ+mSoHt4jiQwZmdLEOFjETE2pCLsnI/njM7THbbXcA+lSIG5AJ6O1iHvRmFSPJDJDjoV9K6Apxkjq8h3Rlx1oSw8rHDJBETO7FsJjp4nmfH8ZnHo39J8soalJII3Efbf/athjcPBJ1eqDxiXjJNxsuecViYvPyVQXi7HT1QV3qjndofdYaUcXCx2ZTLWwLnqJiHXftwLmzoHzH4KzfuGbp0G0qe5QfElbUZJG4r7H3z+xYHBwv3t1MXTrm9xxGUJTXwk5Lotxt+jWR9LXnUzpRndY7RYd8bt3JAzSou8RsiyxuYBY7SF48Xo47w8w5uzW6zweKXWchKqi6SPuFbv8t1k9BgWPmKk+aOrKOAk3W+75A5wfClniMnEf2oEiYnFZ7r65iAOrO/b+ULx1F4yZCUdcHHz9nOc77kqKgfQR98N7AsQ9hOVuImWchRsTmCwKhiSvB2dHcYu/3WLIcbB3WfBgiFDE43O3/jd2xp1vXSC+9jN/Zt8+O0gaiXtbn7txyzie+gppIuFGeg6D5tSVUYqK0o3ix3YLuQVSa33fsui293p9v/shHTte4QhASThkrBO5wWiqhzfvhHPvl9j9FJMe4t5UJ7fIlsulwEyouoK6Cv9Ek9soHAHepqTVCekQbrPcQeq774jSNVN9UCZiOyqkmTk+PdD2TKp+/icpazB2Vvz7soH0EPfDe8UHatVz7jFIxL1t0w5juTuLunIJKXQjXXvztdXnRBqq5P/bI/Hx1LYy4lTY9lF028YzmWphlSEo3RTffsq2wsK/w8zfxbcfG0kTcd/d+iTO7iq+3Lbp4dUHjbg7CTe7Zbr0ALRM6DmR0s0iXNE2sHAKw06EfctlPiYS8fjbLfofJct46qxrLe6Yk36YlOSkaHHZNx+CtuIO8qWXt0lOqDYTqo6irsK9lrtSkJEdv8WXKEo3uc8lA2KYDToGtn8Sedt4ImUs+h4py30rOr6PNf8WbTn22/GNxWbSRNz3tL9iFg5vXRSoqU6K9bitdng6U+9inztAVtfkNnuIhZKNUOSiydRARp0p9VciYYdbxroAdrT0b105vPtTmP2gVDh1EOkh7lYPxUB6DmudVmz522OtQWFIDFrLD8OtbhmQGP1wFUhTSekm6O1Cyx184v5B5DaG5Tvjd8tYse6H97afo4uGt+6GcbOlfILDSA9xL9vavvJdW7eMcck4i8Ya8GRJxIJbyesl3b+ciFvdMiDhm0rBwbXht+tIB6a25PaUiBtvU/hqssFYNw/2LJHyAg4kTcQ9SAPgnm3cMmYy1Vm43SUDcj4loXRrzLQ0iVVbODLVI+kYSsG482HDG6G3aW6UpMT8QaG3iRaramaki0kgFbvhzR/CxX93REx7MNwv7rWH5HaqbQOOdm6Zg6YxtpOoc3GkjEX+ACkC5TQObZexZXVJ9Ug6zvjzYf3rodcf3i3VX+1oHzjoGFnuXxnd9i1N8PI34YTbYfAx8R8/Qbhf3Mu2SMhXW196935y699QJc+rDvh7XxpSj5tj3C0KhvrPLydRusldmanBGDxd7orKtgZfX2GDv91i4NGy3P1VdNt/9iDkdIPjb7fn+AnC/eJeGsQlAyL2PYf6XTOV+4y4Owk3x7hbFAyWDFWn1Zgp3eifKHQrngwYPzu09V6+I/5IGQsrHDIat8yBNbDwEbjgL47PIXD26KKhbEvoEznQ7161T25VDc7AzaUHLLr2lvC3yv2pHklrSje7NwwykHCuGTti3C2KxoDKkGzjcHdiXi/Mux3O/Dn0GGjPsRNIeoh7rxATR4F+90oj7o6i3sUJTBZ5vQAFVQ4T9xKXFQwLxbCT4NDW4O0MO9IUOxSZ2f4kyIPrQm+34lnwZMLka+05boJJA3EPEgZp0WuknBwg1pVxyzgHt8e4A3QtAt3iLHH3etNH3DOyYMys4FEzdsS4B2KVITiwKvj6unL44Jdw7gOOd8dYuGOUofB6JUMwVMhXr1HSr7ChGloa3O8GSCfcXHrAIrdQIieCVSBNFeXbpa1eumRih3LN2BHjHsjg6bLcszj4+gW/hXHnwYDJ9h0zwbhb3A/v9iUhdAu+vmi0xMBX7ReXjMlOdQ7pEOeekSnhhk4qQXBgtX+CMB0YeRrsXyXN7S0aqqSWftvw53gYMEWWuxe1X3dgjdSPOeNe+46XBNwt7gdWQb8wJ3L3AWK1l26RxwbnkA5x7iAWcmCyXKo5uDa9xD0rF0adDhve9L9WvlMadNhprA2YDCj5LgOjn7SGt++BU++BvEL7jpcE3C3u+1b4r7jB8Hig1wjYvwLyjb/dUaTDhCpAXu/gE36p4uAaf+PndKGta+bQNomEs5Psrj4fvm5dIXLbArnzn/oNe4+XBFwu7suhfwQfWK/RMsFkImWcRV25+90yIJP0NQcjb5csDq6BfhNTPQp7GX027PpK7vZAXK2JiOMfeoIsLdeM1vDBfXDaT+zJhE0y7hV3rcUijzTBUTQaKnYYt4zTSBe3TPd+UufECZmq9YehpszeKBInkNMdhs2Aze/K80S1Dxx2kiy3LZDlxrfA2wwTLrL/WEnAveJ+eI/EnEYKb+w12jehatwyjkFrEaJ0iOjo3k/ExwmumYPrpIenJyPVI7Gf8RfA+nnyOFEVL60aM/uWyzn6+Z/gpDtdE/rYFneOGvwumUiTKkWjoO4w5Ds/o6zTUF8hPk6HNTfoEPkDpGyxE8IhD6wOH2DgZsbOgm0f+wMkEuGW6TVSJnAbKmHda1LbZvwF9h8nSbhX3KNxyYDEujfXmXK/TqK6RMLYvC2w5hV49lKYfxfsDhFj7GTyBwIKKh0g7vuWhQ8wcDN5hfLZ1r4i/u9ERK4oBQN8RcQ+/YNUfXTxXZB7xX33Ihg4LfJ2Gb5mEM31iR2PIXpqfI1TXrsNPv8zTLpK3Bv/uhbe/V9JDHILPQZCS6MzLPe9y/zilI5MuEDizRPZhGTsebIsXg9HXZW44yQBd4p7/WFxywybEXnbw7shM9e5jYw7I9XFIoh7FsE35sOky6Vz/Hc+h+J1MPcaaKxN9SijI38ANFanXtwbqmQMfcandhyJZNxs2L3Q/jDIQEaeKkulICsvccdJAlGJu1JqplJqo1Jqi1LqniDrf6iUWqeUWqWU+kApZWNecBC2fQSDj42uA4qVjl0cpiCQIblU7JRkm0sebf0ddi2COXMlimbuHHdY8F0KZPIt1YlM+1dKfHs6zGOEons/X25EhN6q8VA0FlBifJRtSdxxkkBEcVdKZQB/BWYBE4A5SqkJbTZbDkzTWk8CXgbut3ugrdj8rsS+RkO5r3pcuGpvhuSy5QOJYho4tf26jCy46GGJhHr7x8kfW6woBd37SpP2VLI3jf3tgeQWJva3vPVDiX4CMSJdTDSW+3Rgi9Z6m9a6EZgLXBi4gdZ6gdbauo/+CrChsWEIvF7Y/B6MPiu67ct3yK1q8fqEDckQA0310lR47MzQ23gy4LIn5ce15pWkDa3D9BgqbRy9Lakbw75l/o5C6Uxdhdz5BbbQtJNl/5BKlADrw/RwdQHRiPtAILAt+B7fa6G4CXgr2Aql1K1KqSVKqSUlJSXRjzKQA6vkyhqqhntbKnaKhVi+XZJNDKll1b8gu1vkzOIuPeDiR+CtuyW6xskUDBb3UmUKY93TfTIVpF9yQyVMvgaWPm3//qsOwI5P4eQ75fmuL6Cpzv7jJAlbJ1SVUtcC04AHgq3XWj+qtZ6mtZ7Wu3cHK7r1mwTXz4t++/KdEhPbY7CkLRtSy/J/Qm4PiZaJxKBpMHkOvH134scVD/kDICc/cdZkJKoOSpBBqL4G6cLBtdB3Aky/GZY907pSpB2seA4mXCi18AtHit9928f2HiOJRCPue4HBAc8H+V5rhVLqTOAnwAVa6wZ7hhcEjye2FlflOyQdu+8E43dPNWVb5ftoaoi+XOsp98CuhbDzi4QOLS56DISMbLk7TAW7F0o9cpdmUkaNVfGycARMvBw++p19+25plruBqTfK84mXy3L1S/YdI8lEczYsBkYrpYYrpbKBq4BWprNSagrwd0TYi+0fZgepPywRF3m9oM8EKI6iAa4hcax+CY64xB/nHg3ZedKz8u17ZL7FieQPBFIYMWOJe7pzcLW/4uUpd0tCk10G2/p5Un/KmuSf4MtM3fR2audS4iCiuGutm4HbgHeA9cCLWuu1Sqn7lFJWbu4DQDfgJaXUCqVUDH6TBGK14lJK2mjtX5nqEXVetBZ/+/jZEgkTTRirxcTLJBlt5fOJG1885A+A5obUuWV2L4TBx6Xm2MnkQEDFy6694Kz74KUb4i/apjV88RDM+L7/tT4T5O6ysRp2fRnf/lNEVPdxWuv5WusxWuuRWutf+167V2s9z/f4TK11X631ZN+fMwoyBLbi6j9Z6jTrBMbIGkJjXVi79YduMc63KAUzfyc9LJ1QfbEt+QMliiMVbpmmOnFXpHukTEuzlO4OTNKaci0MOQ7+821Z31G2fyI1a6woGZBzbtKV8njJUx3fdwpJbyddRUAT3fz+UuAp1fHInZX1r0sRptoS6BqlSyaQQVNhxKlS88Np5PYE5ZEmEsk2HvYtlwnAWO6E3Mihrf4KnIHMekA6J736nY65T7wt8O5PpNNS2zmLo2+Q5frX3ZMxHUB6i3vpJpl8sRgwRX4MhuRjiXt1DP72tpz5M5n0SpX7IxRKicBqrzQhSSY7v+gcLpn9IVpqZnWBq56XeZy5V8s8WywsfQpyesCRl7Zf13uMZKy2NMAG98W8p7e4F7+U7roAABQxSURBVG8Q35mFEffUULJR3CkDpkBNSccbG+cPgOO+B+/9r73js4PeY8WCT/aFZ9tHckeT7uxZ7K+33pbsPLj6JXGPPX6mNPOIhkPbYcFvYdb/hS4dPv0WWX71cOxjTjHpK+5at/fRDZgipYINyWX9676JVE98ljvACbfBvpXSds1JFI2GzC7J9bs31kjyUjQF9NzOnkUwKExEUGY2zP4jHP89eHKmlBEIR2MtvHgdnPyj8DXwJ14uJTH2LZO5DReRvuJeuU987IF1n/tP9ndZMSSP9a9Lk2OAqn2Ru2eFIytXoho+f8iesdlF0Vjx3x7alrxj7vxCehq09UOnG011YqhF079h6o1wxTPwyq1SHjjo/urh5W9A7/Fw7LfC7y+3AI6aI48/+X1Mw0416SvuJeuhz7jWr3XrLf41l1d7cxUVu6Ts8hBf8+HynfH3+Jx8Dez+SpKinELRGHE9lWxM3jG3fggjTkve8VLFvhXi9srKjW77YTPgulfh3Xvh3Z+2LjtyeA+8cKUYfhf9LXInN4AZP5DlutckG9glpK+4F6+XK3Nbhh7v7GzHdGPDm9IizeoeX74DCuOsx52dB1O/AV/9Le7h2UbPoTKZl8zS0lsXwMhOIO6RXDLB6HckfOsTKNsGDx4Br34X/nUdPHKi7OvSJ6Mvj9xrpFxEdQt89NvYx58i0ljcN7S33AGGnmDEPZlYUTIgiT7VByHfhqKh02+RjNfaQ/Hvyw4ysuSOpGxLfDHX0XJou0xOd4Yyv7sXdSwDt2svmPM8fPNt+T8dcRF85ws4/Sd+YyNazv6VLJc9I3efLiB9xb1kfetIGYuhM4y4J4vqYskqHH6KPK/YLREvsf6wgtG9n3TmWfJE/Puyiz7jpJlEMvzu6+f5Jqnd2+MzKrze+Msr9BopxsCRl8r51xH6HQnjzhPr/f2fdXwsSSQ9xd2KlOkdxHK3GmabZKbEs+bf4pLJ6iLPrSJudnH892DRY3JH4ASKxkqp4mS4Zta+ChMuSvxxUs3BNTJhXDAk1SMR61155H/vgv4Q6SnuZVukY0tuQft1SsGQ42GnO+tFuIqVc2HSFf7n5dvt7X/Z9wi5O1v9sn37jIeBU6VMbMmGxB6nYpdkXw87KbHHcQLbFsDI01M9CqFwBBx1NaBd0SUsPcU90m3c0Bmw45PkjaczUrJRmh+MONX/mt2WO8Dxt8nEqhPCWwcfK66oRMdDr30Vxp5rj3vL6Wxd4KyIoDP+VwrfbVsAuxenejRhSWNxPzb0+tFnweb3nVtCNh1Y9S+p5hjoE06EuI86A7zNsN0BTRW69pIm3wdWJe4YWsPKF+CoqxJ3DKfQVC+ZqcMddIfSvR8c+215/MYdzjAqQpCm4h5hdr3XSMjpBgdMCeCE0NwIy5+VePRA7Ihxb4tScNx34UuHhEUOPVFiqZvqE7P/fcuhqVbuPtOdXV+K261Lj1SPpDWn3C2tIg+uldh3h5J+4l5XIT+uvmFSigHGzIRN7yRnTJ2Nda9J0knfgGglrX0+92H2H2/SFZIeXrLJ/n3HyrATILt74noHLH8WJl8bXfKN29nwJow5O9WjaE+XfDjzF/J4/o+cM6HfhvQT9z1LJKY1kj9yzDnSZcVgPwsfgelt0rqriyUWPNgkd7xk5cK0b8JCBxR3GnwseJsk8cZuGmul+1BncMl4WyTcc8LFqR5JcKbeCD0GSTXKrx5J9WiCkn7ivvur0NXjAhlyvCSCVO5L/Jg6E7sXywk/dlbr1/ctl9o+ieKYmyX0sqYscceIhqIxEi63dYH9+17xnLhjCgZH3tbt7F4o1UOLHNr0OyMTzntQHn/0W+ck0wWQfuK+6R2ZZItERpYkwTgljC5d+Oi3cOJ/tU+u2bvE358yEXTrI5mwC1NsRSkF484VcbJzss3bAl/+FU643b59Ohk3xPGPPksMyeY6ePPOVI+mHekl7hW7xN8ebfOCyXMk8sDBM96uYvciqaU9+dr26/YuhUHTEnv8k38Eix+DmtLEHicSU26A5nopmGYXG96QSJxwUWDpQkuTzNtMuDDVIwmPUnDRwxIaufYV2DA/1SNqRXqJ+4b5rYtURWLICdI7MZGha50FreGD++DkO6W2diBer4h7Ii13kOJdEy+HT/+Y2ONEYshxvh/8f+zZX0sTfPhrOOnOzjORWjhCOiE5naLRcIavHMErt0iJDYeQZuL+htR/iBaPRyanVjyfuDF1Fla/DPUVwa32Q1ul1HI8TTqi5aT/hlVzk1t6ty0ej1zI7HL5LX5caqKMmWnP/pzO4sdh+s2pHkX0HP89qTTZWA3PXChNVBxA+oh7dYmEn8WazTb1Bkm4ceCEiGuoK5e62bP/FPyuac8SaXCdDLr3hVPugdfvSG2S2kl3woHV8Z9Xlfvgkwdg5u86h9V+cJ249sadn+qRRI8nA67+lyQ4HdoKT88Wj0Cqh5XqAdjG0qekpGd2Xmzv6zFIugS5sEeiI9AaXv+B+EdD+dT3LEq8SyaQY26SrNVFjybvmG0ZdYbEQ793b8f30dIML39TMiKDla9ORz57UL6/tq49p5NXCDe8KQlX+5bB46envDRweoh7cyMsfsKfFhwrJ/5QbgXrKuwdV2dg2T+kUNtZ9wVf723xJaMk0aXgyYBLHoVPfw+7FibvuG2ZeLnUnK8ujv29Wksj8Kw8cTV1BvavlDISx30n1SPpGEWj4JYFkFckbsG/ThejMbATVBJJD3Ff+x9fRuQRHXt/4XCxPD8IIVCG4OxeBB/8Ei570l/Wty07PoNufWXiKZkUjoAL/wYv3SD5DKlgynXSNPuVW2N3EX3yAGz7GC59XHz46Y7W8P7PJeLJzT1he42E2xaLe7i5Ht6+B/44Dj77U9JzMNx/1jTWwke/gRN/EN9+zvw5bJxvSgFHS/kOaVt20cNyYQ3FmpelgFgqGHO2+L6fuTA1yWr9j4K8XlId85MHonuP1rDgtzIPdN1/Wjd4T2dWviD/p6NvSPVI4ievUL67K/4J+QOhtkwafPx+FDx2uhhE2xJf6M794v7JA1JuIN6az7kFMOt+ePU7MkFoCE3FLvjH+XDyf4ev/dHcKG32jrgkeWNry/RbxIf75DnJrz2jlBgduQWw+kVY8JvwORXNDfDGD8TI+MZbMjncGSjfIRPylzzmPl97KJSCCRfAD1bDnLmSn6C1hAR/+nv49A8JH4K7xX3nF+Lznfk7e/Y34QKJk//3zeIrNrSndDM8fR4c+x0RznAsfUomUlOdLj/jDomgefpcWPNKco896So4vBfO+Y1kTz9/JVTub79d6RZ46lxJwLrxjeSEjTqBugp4YQ6cfJe0sks3PBmiKTe9C/+1BkadKYXlRie+IJp7xX3/KnELXPqEhCDZxVm/lEiLebcbgW/Lto/gqVnyQzz+u+G3rT0EH98v/08nMOUamPMvsZ5fmCNhiskgMxtO+qH8L258U1w1fztOOvlU7pPJ1vfuhSfOEvfVlc86r8RtomiogrlXS4/dY78VeXs3s+MzeOYiyO4qIn/CbQk/pNIpSr2fNm2aXrJkScfevPpleOsumP1gYlKUG2vEwureDy74f1J1sDPTWAsf/w5WvQgX/x1GnBJ+e63h9e9LlubsB5MzxmhpqoMlT8Hnf4bBx0gdnAFHJzaG3OsVESsYAufeD2XbJBJm0zty3FFnwqwHoGBQ4sbgNA7vgeevkvyH8x5M30njmlJ472fSuWnW/dLUPE6UUku11hFreUQl7kqpmcCfgQzgca3179qszwGeAaYCZcCVWusd4fbZYXE/uBZevF4iNPofFfv7o6WxRqz3kk1w8SPpecsYiZYmuZAu+LUUSDr3AalvEokPfwUb34YbX4fcnokfZ0dorIUlT0otGk+WhC1OuECaXNspNFpLv9NdC+Htu8VQqDsM/SbC6DPFz77+DWiqkbmJkaeJfzZdDYqWJlj6tL/A3PG3pWdyVtlWOb+WPwuTr4bT/se2KCDbxF0plQFsAs4C9gCLgTla63UB23wXmKS1/rZS6irgYq31leH2G5fl3tIkVR0TjdZyIi74tYQ2Tfum1A1Jx5PRoqleau1snC+Weq+R0nlm2ImR31u5T0K/SjfDDa9HdyFINVpLBu3ql6S+f0OlpJIPmCKWdsFg6N5fQhozu0BmjvyBnIctjWII1JVL+YWqAyLmFbvl/3BwjXTt6Xck9BoF2z+V95/1Cynfq5SM4cAqWDcPtn8CxevEcOk3UToR9RkvURfd+rqzb6rWInbr/gNLnoZeI8SK7TM+1SOzD28L7FsBW96Dze/JJPFRV0mXsB4DbT2UneJ+PPBzrfU5vuc/BtBa/zZgm3d823yplMoEDgC9dZidxyXuyab+sNzKr3hefsBDZ8iPrmiU/GDziiQiwqnWltYSc9tQ1f6vplhEuXKvpH6XbJDPNOJUmHRl+DuWxlqpfLh3qQjj1o/g2Fsl6SZU3LvTqTog5Xr3rxTXQcVuqD4oFnZzvW9ZBygxMDxZ0rIxt6f8de3tuygMkQtj34nSW9WipVkiZz75PaDFJdN7nNSBLxwu/nbtK7R2cK3/O6ncJyF1eb3EXditD3Qp8B3Xt+xSIGPJyJaxZWTL+KzHGdkywac84jLzZIDKCHjNeh64Loa7mJYmXye03fK/K9sin2OP73c+fra0Xhx4tJ3fWPJoqvP9VvZB1X5Zlm32fUcbxRAYdab8DT3BbwTYjJ3ifhkwU2t9s+/5dcCxWuvbArZZ49tmj+/5Vt82IWuvdljcK3ZJQgDaF1bmG7/1+OvPo79eFd22bR+H2LaxRn5kDVVSKKixRqy3liaxwjyZ8qP42rpXrS19y1L7enyB+1fw9aYq4Hnbx7S5e1C+fXjlz+v1P7b+VIAYfb3MhIwuclHKypV0+S4F8hkIOC9amkTYmmrFsm+qlZO7sUYKWvWfLH74Iy7uPJOB8WJZ69s/hdKNYuUf2i7nVXOdWPs53UUgPFk+wc0EvPLer79bDbpFLEdvk1w8tJdW50Pb7QPP8WBLreU4rbDO47Z3rW1+H8rjO7eyZTI5u6tEh2TlynlnXTC+vqgEXFxCjcn6f4UcN60fx/X+gKV1rjdWiyGjPHJhzR8gf937S7Jc3yPkLiRJ53604p7Uezyl1K3ArQBDhgzp2E4yu/hv56yTrZ2QqtbrO7QtkbdVngCLxyNRNk21Et+tWwKEttkvuN5mQLfex9c/GO3LZGz7YwwQbWsdyve68u/PEgDrApNhWWDWMuDztP184Z57MiQNPrOLLLNy5cTuWpTeLqpEopS4XoLNG3lbRFDqK+VOwdsswu1tFvH++nFTgKg3+d4cymghvDETeB4HWvGB577vVAMt51hmF8jKEQMhM1u2117/xebrpdc3zuY267ytt2n1G227pP1YQv4uo3m/CvL+Nttk5crFKStPLrYui8GPRtz3AoGByoN8rwXbZo/PLdMDmVhthdb6UeBREMu9IwOmW5/I8dUGg5vxZIgVaO6CDHEQjUNtMTBaKTVcKZUNXAXMa7PNPMDKG74M+DCcv91gMBgMiSWi5a61blZK3Qa8g4RCPqm1XquUug9YorWeBzwB/FMptQU4hFwADAaDwZAiovK5a63nA/PbvHZvwON64HJ7h2YwGAyGjpKmaWEGg8HQuTHibjAYDGmIEXeDwWBIQ4y4GwwGQxpixN1gMBjSkJSV/FVKlQAdbQ9eBIQsbeAyzGdxHunyOcB8FqcSz2cZqrXuHWmjlIl7PCillkRTW8ENmM/iPNLlc4D5LE4lGZ/FuGUMBoMhDTHibjAYDGmIW8X90VQPwEbMZ3Ee6fI5wHwWp5Lwz+JKn7vBYDAYwuNWy91gMBgMYXCduCulZiqlNiqltiil7kn1eDqKUupJpVSxr4uVa1FKDVZKLVBKrVNKrVVK3ZHqMXUUpVQXpdQipdRK32f5RarHFC9KqQyl1HKl1BupHks8KKV2KKVWK6VWKKVc0p+zPUqpAqXUy0qpDUqp9b42pok5lpvcMtE063YLSqmTgWrgGa11mEalzkYp1R/or7VeppTqDiwFLnLpd6KArlrraqVUFvAZcIfW+qsUD63DKKV+CEwD8rXWs1M9no6ilNoBTAvXutMNKKX+AXyqtX7c1x8jT2tdkYhjuc1ynw5s0Vpv01o3AnOBC1M8pg6htf4EqX3varTW+7XWy3yPq4D1gL3t3pOEFqp9T7N8f+6xftqglBoEnAc8nuqxGEAp1QM4Gel/gda6MVHCDu4T94HA7oDne3CpkKQjSqlhwBRgYWpH0nF8bowVQDHwntbatZ8F+BNwF+27XbsRDbyrlFrq68XsRoYDJcBTPlfZ40qprok6mNvE3eBQlFLdgH8DP9BaV6Z6PB1Fa92itZ6M9AqerpRypctMKTUbKNZaL031WGziRK310cAs4Hs+t6bbyASOBh7WWk8BaoCEzRu6TdyjadZtSDI+//S/gee01q+kejx24LtdXgDMTPVYOsgM4AKfr3oucLpS6tnUDqnjaK33+pbFwH8QF63b2APsCbgbfBkR+4TgNnGPplm3IYn4JiGfANZr/f/bu0OUDKIoDMPvEYtYDIoIBpuLsAiCq9DgAlyAFnfgDgwGFf5iNbkJi8miwV18hrlV+Bn5GefyPmmYMqfMx+XcAye3U9fzF1W1U1Vb7XmD4eL+fdqqxklylWQ/yQHDf/Ka5Gziskapqs12WU9rY5wCs5syS/INfFbVYXt1Aqxs8GCpHar/xW/Luicua5SqegKOge2q+gJuktxNW9UoR8A58NZ61QDXbe/u3OwB920qaw1YJJn1CGEndoHn4RzBOvCY5GXakka7BB7a4fQDuFjVh2Y1CilJWs7c2jKSpCUY7pLUIcNdkjpkuEtShwx3SeqQ4S5JHTLcJalDhrskdegHIXMySgxdYyAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def logistic(f):\n",
    "    return np.exp(f) / (1 + np.exp(f))\n",
    "p_grid = logistic(f_grid)\n",
    "plt.plot(x_grid, p_grid, 'C1', linewidth=1)\n",
    "plt.plot(x_grid, p_grid[:, 1], 'C1', linewidth=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3. Sample from a Bernoulli:__ for each observation point $X_i$, the class label $Y_i \\in \\{0, 1\\}$ is generated by sampling from a Bernoulli distribution $Y_i \\sim \\mathcal{B}(g(X_i))$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Select some input locations\n",
    "ind = np.random.randint(0, 200, (30,))\n",
    "X_gen = x_grid[ind]\n",
    "\n",
    "# evaluate probability and get Bernoulli draws\n",
    "p = p_grid[ind, 1:2]\n",
    "Y_gen = np.random.binomial(1, p)\n",
    "\n",
    "# plot\n",
    "plt.plot(x_grid, p_grid[:, 1], 'C1', linewidth=2)\n",
    "plt.plot(X_gen, p, 'C1o', ms=6)\n",
    "plt.plot(X_gen, Y_gen, 'C3x', ms=8, mew=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation with GPflow\n",
    "\n",
    "For the model described above, the posterior $f(x)|Y$ (say $p$) is not Gaussian anymore and does not have a closed form expression. A common approach is then to look for the best approximation of this posterior by a tractable distribution (say $q$) such as a Gaussian distribution. In variational inference, the quality of an approximation is measured by the Kullback-Leibler divergence $\\mathrm{KL}[q \\| p]$. For more details on this model, see Nickisch and Rasmussen (2008).\n",
    "\n",
    "The inference problem is thus turned into an optimisation problem: finding the best parameters for $q$. In our case, we introduce $U \\sim \\mathcal{N}(q_\\mu, q_\\Sigma)$ we choose $q$ to have the same distribution as $f | f(X) = U$. The parameters $q_\\mu$ and $q_\\Sigma$ can be seen as parameters of $q$, which can be optimised in order to minimise  $\\mathrm{KL}[q \\| p]$. \n",
    "\n",
    "This variational inference model is called `VGP` in GPflow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
      "  Objective function value: 11.678611\n",
      "  Number of iterations: 150\n",
      "  Number of functions evaluations: 157\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
      "  Objective function value: 11.678611\n",
      "  Number of iterations: 150\n",
      "  Number of functions evaluations: 157\n"
     ]
    }
   ],
   "source": [
    "m = gpflow.models.VGP(X, Y,\n",
    "                      likelihood=gpflow.likelihoods.Bernoulli(),\n",
    "                      kern=gpflow.kernels.Matern52(input_dim=1))\n",
    "\n",
    "o = gpflow.train.ScipyOptimizer()\n",
    "o.minimize(m);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now inspect the result of the optimisation with `print(m)` or `m.as_pandas_table()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>prior</th>\n",
       "      <th>transform</th>\n",
       "      <th>trainable</th>\n",
       "      <th>shape</th>\n",
       "      <th>fixed_shape</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>VGP/kern/lengthscales</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>+ve</td>\n",
       "      <td>True</td>\n",
       "      <td>()</td>\n",
       "      <td>True</td>\n",
       "      <td>1.6355003192882445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VGP/kern/variance</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>+ve</td>\n",
       "      <td>True</td>\n",
       "      <td>()</td>\n",
       "      <td>True</td>\n",
       "      <td>32.92700076548122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VGP/q_mu</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>(none)</td>\n",
       "      <td>True</td>\n",
       "      <td>(50, 1)</td>\n",
       "      <td>True</td>\n",
       "      <td>[[-1.1196742258326438], [0.2620987093978069], ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VGP/q_sqrt</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>LoTri-&gt;vec</td>\n",
       "      <td>True</td>\n",
       "      <td>(1, 50, 50)</td>\n",
       "      <td>True</td>\n",
       "      <td>[[[0.45544562836404157, 0.0, 0.0, 0.0, 0.0, 0....</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           class prior   transform  trainable        shape  \\\n",
       "VGP/kern/lengthscales  Parameter  None         +ve       True           ()   \n",
       "VGP/kern/variance      Parameter  None         +ve       True           ()   \n",
       "VGP/q_mu               Parameter  None      (none)       True      (50, 1)   \n",
       "VGP/q_sqrt             Parameter  None  LoTri->vec       True  (1, 50, 50)   \n",
       "\n",
       "                       fixed_shape  \\\n",
       "VGP/kern/lengthscales         True   \n",
       "VGP/kern/variance             True   \n",
       "VGP/q_mu                      True   \n",
       "VGP/q_sqrt                    True   \n",
       "\n",
       "                                                                   value  \n",
       "VGP/kern/lengthscales                                 1.6355003192882445  \n",
       "VGP/kern/variance                                      32.92700076548122  \n",
       "VGP/q_mu               [[-1.1196742258326438], [0.2620987093978069], ...  \n",
       "VGP/q_sqrt             [[[0.45544562836404157, 0.0, 0.0, 0.0, 0.0, 0....  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.as_pandas_table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this table, the first two lines are associated with the kernel parameters, and the last two correspond to the variational parameters. Note that, in practice, $q_\\Sigma$ is actually parametrised by its lower-triangular square root $q_\\Sigma = q_\\text{sqrt} q_\\text{sqrt}^T$ in order to ensure its positive-definiteness.\n",
    "\n",
    "For more details on how to handle models in GPflow (getting/setting parameters, fixing some of them during optimisation, using priors...), we refer the reader to the [notebook on models](../understanding/models.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictions\n",
    "\n",
    "Finally, we will see how to use model predictions to plot the resulting model. We will replicate the figures of the generative model above, but using the approximate posterior distribution given by the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3, 3)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "# bubble fill the predictions\n",
    "mu, var = m.predict_f(x_grid)\n",
    "plt.fill_between(x_grid.flatten(),\n",
    "                 (mu + 2 * np.sqrt(var)).flatten(),\n",
    "                 (mu - 2 * np.sqrt(var)).flatten(),\n",
    "                 alpha=0.3, color='C0')\n",
    "    \n",
    "# plot samples\n",
    "samples = m.predict_f_samples(x_grid, 10).squeeze().T\n",
    "plt.plot(x_grid, samples, 'C0', lw=1)\n",
    "    \n",
    "# plot p-samples\n",
    "p = logistic(samples)  # exp(samples) / (1 + exp(samples))\n",
    "plt.plot(x_grid, p, 'C1', lw=1)\n",
    "\n",
    "# plot data\n",
    "plt.plot(X, Y, 'C3x', ms=8, mew=2)\n",
    "plt.ylim((-3,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2D example\n",
    "\n",
    "In this section we will use the following data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.loadtxt('data/banana_X_train', delimiter=',')\n",
    "Y = np.loadtxt('data/banana_Y_train', delimiter=',').reshape(-1,1)\n",
    "mask = Y[:, 0]==1\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(X[mask, 0], X[mask, 1], 'oC0', mew=0, alpha=0.5)\n",
    "plt.plot(X[np.logical_not(mask), 0], X[np.logical_not(mask), 1], 'oC1', mew=0, alpha=0.5);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model definition is the same as above, the only important difference is that we now specify that the kernel operates over a 2D input space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'STOP: TOTAL NO. of ITERATIONS REACHED LIMIT'\n",
      "  Objective function value: 109.143688\n",
      "  Number of iterations: 25\n",
      "  Number of functions evaluations: 27\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'STOP: TOTAL NO. of ITERATIONS REACHED LIMIT'\n",
      "  Objective function value: 109.143688\n",
      "  Number of iterations: 25\n",
      "  Number of functions evaluations: 27\n"
     ]
    }
   ],
   "source": [
    "m = gpflow.models.VGP(X, Y,\n",
    "                      kern=gpflow.kernels.RBF(input_dim=2),\n",
    "                      likelihood=gpflow.likelihoods.Bernoulli())\n",
    "\n",
    "opt = gpflow.train.ScipyOptimizer()\n",
    "opt.minimize(m, maxiter=25) # in practice, the optimisation needs around 250 iterations to converge\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now plot the predicted decision boundary between the two classes. To do so, we can equivalently plot the contour lines $E[f(x)|Y]=0$, or $E[g(f(x))|Y]=0.5$. We will do the latter since it allows us to introduce the function `predict_y`, which returns the mean and variance at test points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_grid = np.linspace(-3, 3, 40)\n",
    "xx, yy = np.meshgrid(x_grid, x_grid)\n",
    "Xplot = np.vstack((xx.flatten(),yy.flatten())).T\n",
    "\n",
    "p, _ = m.predict_y(Xplot)  # here we only care about the mean\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.plot(X[mask, 0], X[mask, 1], 'oC0', mew=0, alpha=0.5)\n",
    "plt.plot(X[np.logical_not(mask), 0], X[np.logical_not(mask), 1], 'oC1', mew=0, alpha=0.5);\n",
    "\n",
    "plt.contour(xx, yy, p.reshape(*xx.shape), [0.5],  # plot the p=0.5 contour line only\n",
    "            colors='k', linewidths=1.8, zorder=100);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Further reading\n",
    "\n",
    "There are dedicated notebooks giving more details on how to manipulate [models](../understanding/models.ipynb) and [kernels](../advanced/kernels.ipynb).\n",
    "\n",
    "This notebook only covers very basic classification models. You may also be interested in:\n",
    "  * [Multi-class classification](../advanced/multiclass_classification.ipynb) if you have more than two classes.\n",
    "  * [Sparse models](../advanced/gps_for_big_data.ipynb). The models above have one inducing variable $U_i$ per observation point $X_i$, which does not scale to large datasets. SVGP (Sparse Variational GP) is an efficient alternative where the variables $U_i$ are defined at some inducing input locations $Z_i$ that can also be optimized.\n",
    "  * [Exact inference](../advanced/mcmc.ipynb). We have seen that variational inference provides an approximation to the posterior. GPflow also supports exact inference using MCMC methods, and the kernel parameters can also be assigned prior distributions in order to avoid point estimates.\n",
    "  \n",
    "# References\n",
    "\n",
    "Hannes Nickisch and Carl Edward Rasmussen. \"Approximations for binary Gaussian process classification.\" Journal of Machine Learning Research 9(Oct):2035--2078, 2008."
   ]
  }
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